Table 2 The Logistic model that depicts the deterioration of the internal friction angle and the cohesion under dry–wet cycles in silty clay.

From: Experimental study on shear strength and deterioration behavior of silty clay under dry-wet-freeze-thaw cycles

Moisture content/%

Logistic internal friction angle deterioration model (\(R^{2}\))

Logistic cohesion deterioration model (\(R^{2}\))

10

\({D_{DW}} = 25.88 - \frac{{25.88}}{{1 + {{\left( {\frac{{{N_{DW}}}}{{1.18}}} \right)}^{1.21}}}}(0.993)\)

\({D_{DW}} = 55.85 - \frac{{55.85}}{{1 + {{\left( {\frac{{{N_{DW}}}}{{1.77}}} \right)}^{1.18}}}}(0.994)\)

14

\({D_{DW}} = 22.85 - \frac{{22.85}}{{1 + {{\left( {\frac{{{N_{DW}}}}{{1.27}}} \right)}^{1.69}}}}(0.996)\)

\({D_{DW}} = 51.98 - \frac{{51.98}}{{1 + {{\left( {\frac{{{N_{DW}}}}{{1.91}}} \right)}^{1.30}}}}(0.990)\)

18

\({D_{DW}} = 21.06 - \frac{{21.06}}{{1 + {{\left( {\frac{{{N_{DW}}}}{{1.35}}} \right)}^{1.67}}}}(0.988)\)

\({D_{DW}} = 47.26 - \frac{{47.26}}{{1 + {{\left( {\frac{{{N_{DW}}}}{{2.23}}} \right)}^{1.41}}}}(0.986)\)

22

\({D_{DW}} = 15.91 - \frac{{15.91}}{{1 + {{\left( {\frac{{{N_{DW}}}}{{1.40}}} \right)}^{2.43}}}}(0.968)\)

\({D_{DW}} = 40.21 - \frac{{40.21}}{{1 + {{\left( {\frac{{{N_{DW}}}}{{2.75}}} \right)}^{1.53}}}}(0.977)\)

26

\({D_{DW}} = 10.33 - \frac{{10.33}}{{1 + {{\left( {\frac{{{N_{DW}}}}{{1.45}}} \right)}^{2.50}}}}(0.928)\)

\({D_{DW}} = 34.48 - \frac{{34.48}}{{1 + {{\left( {\frac{{{N_{DW}}}}{{3.15}}} \right)}^{1.78}}}}(0.930)\)

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